1) Quizzes are the simplest solution to implement and distribute. How you word the questions can have a huge impact on whether or not they feel too academic, you can try adding humor to them as well. You can also try creating mini games along the complexity of tetris and bejeweled, but a lot depends on how skilled and available whoever writes the code is. From what you've told me, recreating a WoW scale game is out of the question.

2)
The issue here is that a lot of leadership skills are "soft skills" that learned while trying to accomplish an objective task such as: sell x many widgets, rock climbing, building a robot for competition, raiding an orc village, etc.
One T.V show you might want to use for inspiration/reference is Donald Trump's the Apprentice. The way it works is that Trump gives each team an assignment, such as raising $ by washing cars. The team that wins sleeps inside his house, the team that loses sleeps outdoors. Of the losing team, someone gets booted off the show/"fired". None of the people on the show intend to go into the car washing business, but washing cars forces them to exert a lot of the soft skills they will use in the workplace such as keeping a positive attitude despite knowing your team is losing, dealing with people who are willing to climb over their own teammates to get to the top, etc.
If you want to focus on the soft skills, you can have the tasks themselves be completely bizzare (ex: selling one eyed sniggets).

3) You mean like anonymous peer evaluations? What if you had a system where each player had a certain number of points to distribute among their teammates, are not allowed to reward themselves, have to distribute all their points, and are not given enough points to divide evenly among their mates? For personal development, you can have the players create a blog of some sort that they share with their teammates and make a case for why their teammates should give them their points.